Factor. j^2 + 13j + 22 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is j^2 + 13j + 22. In the standard form of a quadratic expression, ax^2 + bx + c, the coefficient 'a' is the coefficient of j^2, 'b' is the coefficient of j, and 'c' is the constant term. Here, a = 1, b = 13, and c = 22.Find Multiplying Numbers: Find two numbers that multiply to 'c' (22) and add up to 'b' (13). We need to find two numbers that multiply together to give 22 and add up to 13. The numbers 2 and 11 satisfy these conditions because 2 * 11 = 22 and 2 + 11 = 13.Write Factored Form: Write the factored form using the two numbers found in the previous step. Since the two numbers we found are 2 and 11, we can write the factored form of the quadratic expression as (j + 2)(j + 11).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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j^2 + 13j + 22

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is $j^2 + 13j + 22$ . In the standard form of a quadratic expression, $ax^2 + bx + c$ , the coefficient ' $a$ ' is the coefficient of $j^2$ , ' $b$ ' is the coefficient of $j$ , and ' $c$ ' is the constant term. Here, $a = 1$ , $b = 13$ , and $c = 22$ .
Find Multiplying Numbers: Find two numbers that multiply to $c$ ( $22$ ) and add up to $b$ ( $13$ ). $\newline$ We need to find two numbers that multiply together to give $22$ and add up to $13$ . The numbers $2$ and $11$ satisfy these conditions because $2 \times 11 = 22$ and $2 + 11 = 13$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ Since the two numbers we found are $2$ and $11$ , we can write the factored form of the quadratic expression as $(j + 2)(j + 11)$ .